Mixture distribution suppose that the joint distribution of the two random variables x and y is a.

Question:

Mixture distribution suppose that the joint distribution of the two random variables x and y is

a. Find the maximum likelihood estimators of β and θ and their asymptotic joint distribution.

b. Find the maximum likelihood estimator of θ/(β + θ) and its asymptotic distribution.

c. Prove that f (x) is of the form f (x) = γ (1 ?? γ)x, x = 0, 1, 2, . . . , and find the maximum likelihood estimator of γ and its asymptotic distribution.

d. Prove that f (y | x) is of the form Prove that f (y | x) integrates to 1. Find the maximum likelihood estimator of λ and its asymptotic distribution. [Hint: In the conditional distribution, just carry the xs along as constants.]

e. Prove that f (y) = θe??θy, y ?? 0, θ>0. Find the maximum likelihood estimator of θ and its asymptotic variance.

f. Prove that Based on this distribution, what is the maximum likelihood estimator of β?

image

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Econometric Analysis

ISBN: 978-0130661890

5th Edition

Authors: William H. Greene

Question Posted: